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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox Interval |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | Name = hendrix comma |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-18 13:00:10 UTC</tt>.<br>
| | | Color name = 19or1, noru 1sn,<br>Noru comma |
| : The original revision id was <tt>255296996</tt>.<br>
| | | Comma = yes |
| : The revision comment was: <tt></tt><br>
| | }} |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">57/56 is a [[superparticular]] interval of about 30.6¢ which makes the difference between [[4_3|4/3]] (about 498¢) and [[19_14|19/14]] (about 528.7¢) in [[19-limit]] [[Just Intonation]]; it is also the difference between 19/16 and 7/6. It is also called the Hendrix Comma, since by tempering it out, one can build an 8:10:12:19 [[hendrix chord]], which has steps of 5/4-7/5-4/3. [[patent val|Patent vals]] which temper out the hendrix comma include those from 9, 10, 12, 16, 21, 22 and 26 edo.
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| 57/56 = |-3 1 0 -1 0 0 0 1> is a comma of the 2.3.7.19 subgroup, and on that subgroup, patent vals tempering it out include those from 9, 12, 14, 17 and 26. The comma defines a rank three temperament on this subgroup. | | '''57/56''' is a [[superparticular]] interval of about 30.6¢ which makes the difference between [[4/3]] (about 498¢) and [[19/14]] (about 528.7¢) in [[19-limit]] [[just intonation]]; it is also the difference between [[19/16]] and [[7/6]]. It is also called the '''hendrix comma''', since by tempering it out, one can build an 8:10:14:19 [[hendrix chord]], which has steps of [[5/4]]-[[7/5]]-4/3. [[Patent val]]s which temper out the hendrix comma include those from {{EDOs| 9, 10, 12, 16, 21, 22 and 26 }} edo. |
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| See: [[List of Superparticular Intervals]]</pre></div>
| | 57/56 is a comma of the 2.3.7.19 subgroup, and on that subgroup, patent vals tempering it out include those from 9, 12, 14, 17 and 26. The comma defines a rank three temperament on this subgroup, called [[hendrix]]. You can also temper it out in a rank-2 temperament in 2.3.19/7, called surprise. |
| <h4>Original HTML content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>57_56</title></head><body>57/56 is a <a class="wiki_link" href="/superparticular">superparticular</a> interval of about 30.6¢ which makes the difference between <a class="wiki_link" href="/4_3">4/3</a> (about 498¢) and <a class="wiki_link" href="/19_14">19/14</a> (about 528.7¢) in <a class="wiki_link" href="/19-limit">19-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>; it is also the difference between 19/16 and 7/6. It is also called the Hendrix Comma, since by tempering it out, one can build an 8:10:12:19 <a class="wiki_link" href="/hendrix%20chord">hendrix chord</a>, which has steps of 5/4-7/5-4/3. <a class="wiki_link" href="/patent%20val">Patent vals</a> which temper out the hendrix comma include those from 9, 10, 12, 16, 21, 22 and 26 edo.<br />
| | == Temperaments == |
| <br />
| | === Hendrix === |
| 57/56 = |-3 1 0 -1 0 0 0 1&gt; is a comma of the 2.3.7.19 subgroup, and on that subgroup, patent vals tempering it out include those from 9, 12, 14, 17 and 26. The comma defines a rank three temperament on this subgroup.<br /> | | This is the [[rank-3]] temperament tempering out the hendrix comma, 57/56. This is simply the most sensible name for this temperament. |
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| See: <a class="wiki_link" href="/List%20of%20Superparticular%20Intervals">List of Superparticular Intervals</a></body></html></pre></div> | | [[Subgroup]]: 2.3.7.19 |
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| | [[Comma list]]: 57/56 |
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| | {{Mapping|legend=2| 1 0 0 3 | 0 1 0 -1 | 0 0 1 1 }} |
| | : mapping generators: ~2, ~3, ~7 |
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| | [[Optimal tuning]]s: |
| | * [[WE]]: ~2 = 1202.4345{{c}}, ~3/2 = 697.4314{{c}}, ~7/4 = 970.3487{{c}} |
| | * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 697.3981{{c}}, ~7/4 = 972.1990{{c}} |
| | |
| | {{Optimal ET sequence|legend=1| 5, 9, 12, 14, 17, 26, 31h }} |
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| | [[Badness]] (Sintel): 0.155 |
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| | == See also == |
| | * [[28/19]] – its [[fifth complement]] |
| | * [[Medium comma]] |
| | * [[List of superparticular intervals]] |
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| | [[Category:Hendrix]] |
| | [[Category:Commas named after composers]] |